09年中考数学第一次模拟试题(5)

中考网 www.zhongkao.com

∴?ACB?90? ， ∴AB?AC?CB?3?2222?3?2?12．

∴AB?23， ∴OD?OB?BC?DC?3， ∴四边形OBCD是菱形． ∴DC∥AB，DC?AB， ∴四边形ABCD是梯形． ···················································· 5分 法一：

过C作CF垂直AB于F，连结OC，则OB?BC?OC?3 ∴?OBC?60?． ··············································································································· 6分

CF33，CF?BC?sin60??3??， BC2211393∴S梯形ABCD＝CF?AB＋DC?＝?23＋3＝． ··········································· 7分

2224∴sin60????法二：（接上证得四边形ABCD是梯形）

OD，△DOC和△OBC的边长均为3的又DC∥AB ∴AD?BC，连结OC，则△A等边三角形 ······························································································································ 6分 ∴△AOD≌△DOC≌△OBC， 3∴S梯形ABCD＝3?S△AOD＝3??4??3＝293 ··································································· 7分 4（3）证明：连结OC交BD于G由（2）得四边形OBCD是菱形， ∴OC?BD且OG?GC． ····························································································· 8分 又已知OB＝BH ， ∴BG∥CH． ········································································· 9分 ∴?OCH??OGB?90? ， ∴CH是⊙O的切线． ·················································· 10分 25． 解： （1）由已知得

y OA?3,?OAD?30?．

C1 B 3A ∴OD?OA?tan30??3??1， O1 E ，0?． ·∴A0，3，D?1········································································································ 1分

??3设直线AD的解析式为y?kx?b．

把A，D坐标代入上式得： ???b?3，

??k?b?0O D F (第25题图) C x ??k??3解得：? ， ············································································································ 2分

??b?3 折痕AD所在的直线的解析式是y??3x?3 ． ······················································ 3分 （2）过C1作C1F?OC于点F，

由已知得?ADO??ADO1?60?， ∴?C1DC?60?． 又DC＝3－1＝2， ∴DC1?DC?2．

∴在Rt△C1DF中， C1F?DC1?sin?C1DF?2?sin60??3．

DF?1DC1?1， 221

中考网 www.zhongkao.com

中考网 www.zhongkao.com

∴C12,3，而已知C?3,0?． ·························································································· 4分 法一：设经过三点O，C1，C的抛物线的解析式是y?ax?x?3? ····································· 5分 点C12，3在抛物线上， ∴2a?2?3??3， ∴a??∴y??????3 233233····························································· 6分 x?x?3???x?x为所求 ·

222法二：设经过三点O，C1，C的抛物线的解析式是y?ax2?bx?c,(a?0)．

把O，C1，C的坐标代入上式得:

?c?0?······································································································ 5分 ?4a?2b?c?3 ， ·

?9a?3b?c?0??a??3?333233? 解得?b? ， ∴y??···················································· 6分 x?x为所求． ·

222??c?0?（3）设圆心P?x,y?，则当⊙P与两坐标轴都相切时，有y??x． ···································· 7分

由y?x，得?233233，x2?3?． ························· 8分 x?x?x，解得x1?0（舍去）

223323323，x2?3?． x?x??x 解得x1?0（舍去）

2232323∴所求⊙P的半径R?3?或R?3?． ························································ 10分

33由y??x，得?

22

中考网 www.zhongkao.com

中考网 www.zhongkao.com

第三次阶段考数学试卷

班级______________ 学号_______ 姓名_____________ 分数__________

(考试时间:120分钟；满分：150分)

一、选择题：（本大题共10个小题，每小题4分，共40分）每小题只有一个答案是正确的，

请将正确答案的代号填入题后的括号内。

1．2的相反数是（ ）

（A）－2 （B）2 （C）2．计算6m3?(?3m2)的结果是（ ）

（A）?3m （B）?2m （C）2m （D）3m

3．重庆直辖十年以来，全市投入环保资金约3730000万元，那么3730000万元用科学记数

法表示为（ ） （A）37.3×105万元 （B）3.73×106万元

（C）0.373×107万元 （D）373×104万元 4．在下列各电视台的台标图案中，是轴对称图形的是（ ）

11 （D）? 22

（A） （B） （C） （D）

5．将如图所示的Rt△ABC绕直角边AC旋转一周，所得几何体的主视图是（ ）

A C5 题图B?

6．已知⊙O1的半径r为3cm，⊙O2的半径R为4cm，两圆的圆心距O1O2为1cm，则这两圆的位置关系是（ ）

（A）相交 （B）内含 （C）内切 （D）外切

ABCD1?1的解为（ …… 此处隐藏：1746字，全部文档内容请下载后查看。喜欢就下载吧 ……